We introduce a method for learning provably stable deep neural network based dynamic models from observed data.

Learning-based methods hold the promise ofsolving hard nonlinear control problems inrobotics.

However, wecanmake(9)moretractable (bothforpredictionandtraining) byreducingittoa1-dimensional root-findingproblem: Find ?

This paper explores the application of Hamilton's rule to altruistic decision-making in multi-agent systems. Inspired by biological altruism, we introduce a framework that evaluates when individual agents should incur costs to benefit their neighbors. By adapting Hamilton's rule, we define agent ``fitness" in terms of task productivity rather than genetic survival. We formalize altruistic decision-making through a graph-based model of multi-agent interactions and propose a solution using collaborative control Lyapunov functions. The approach ensures that altruistic behaviors contribute to the collective goal-reaching efficiency of the system. We illustrate this framework on a multi-agent way-point navigation problem, where we show through simulation how agent importance levels influence altruistic decision-making, leading to improved coordination in navigation tasks.